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Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 151 · 40 questions
TalentJR

How to solve it (Same step every time): In an AP the gap (common difference d) is always the same. nth term = a + (n − 1) × d, where a is the first term. Sum of n terms = n × (first + last) ÷ 2; so 1 + 2 + … + n = n × (n + 1) ÷ 2, and the first n odd numbers add up to n × n.

NameDateTime takenScore ___ / 40
  1. 1.What is the sum of the first 8 terms of the AP 5, 7, 9, …? (a) 192 (b) 96 (c) 19 (d) 104
  2. 2.What is the 35th term of the AP 5, 7, 9, 11, …? (a) 70 (b) 68 (c) 73 (d) 75
  3. 3.What is the 31st term of the AP 9, 15, 21, 27, …? (a) 195 (b) 189 (c) 180 (d) 186
  4. 4.What is the sum of the first 9 terms of the AP 10, 11, 12, …? (a) 127 (b) 126 (c) 18 (d) 252
  5. 5.What is the sum of the first 7 terms of the AP 2, 8, 14, …? (a) 161 (b) 280 (c) 140 (d) 38
  6. 6.What is the sum of the first 12 terms of the AP 7, 9, 11, …? (a) 432 (b) 29 (c) 228 (d) 216
  7. 7.Which term of the AP 1, 8, 15, 22, … is 211? (a) 32nd (b) 31st (c) 33rd (d) 30th
  8. 8.What is the sum of the first 8 terms of the AP 2, 6, 10, …? (a) 144 (b) 128 (c) 256 (d) 30
  9. 9.What is the sum of the first 9 terms of the AP 4, 5, 6, …? (a) 73 (b) 144 (c) 12 (d) 72
  10. 10.What is the sum of the first 25 odd numbers (1 + 3 + 5 + …)? (a) 325 (b) 49 (c) 650 (d) 625
  11. 11.Which term of the AP 15, 22, 29, 36, … is 176? (a) 25th (b) 23rd (c) 24th (d) 26th
  12. 12.What is the missing term in the AP 12, ?, 26, 33, 40? (a) 20 (b) 26 (c) 18 (d) 19
  13. 13.What is the 26th term of the AP 10, 12, 14, 16, …? (a) 52 (b) 60 (c) 62 (d) 50
  14. 14.What is the missing term in the AP 8, ?, 24, 32, 40? (a) 17 (b) 16 (c) 24 (d) 15
  15. 15.What is the sum of all the whole numbers from 1 to 79? (a) 3161 (b) 3081 (c) 3160 (d) 6320
  16. 16.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 59 (b) 930 (c) 900 (d) 465
  17. 17.What is the 22nd term of the AP 5, 8, 11, 14, …? (a) 66 (b) 68 (c) 63 (d) 71
  18. 18.What is the sum of the first 12 terms of the AP 2, 3, 4, …? (a) 90 (b) 13 (c) 96 (d) 180
  19. 19.What is the missing term in the AP 4, 11, 18, ?, 32? (a) 32 (b) 26 (c) 25 (d) 24
  20. 20.What is the sum of the first 5 terms of the AP 5, 8, 11, …? (a) 17 (b) 110 (c) 55 (d) 58
  21. 21.What is the sum of all the whole numbers from 1 to 60? (a) 1800 (b) 1770 (c) 3660 (d) 1830
  22. 22.What is the sum of the first 10 terms of the AP 8, 9, 10, …? (a) 250 (b) 125 (c) 130 (d) 17
  23. 23.What is the sum of all the whole numbers from 1 to 65? (a) 2146 (b) 2145 (c) 4290 (d) 2080
  24. 24.What is the sum of the first 5 terms of the AP 1, 7, 13, …? (a) 80 (b) 65 (c) 130 (d) 25
  25. 25.What is the 11th term of the AP 10, 12, 14, 16, …? (a) 30 (b) 32 (c) 20 (d) 22
  26. 26.What is the sum of all the whole numbers from 1 to 85? (a) 3570 (b) 3655 (c) 3656 (d) 7310
  27. 27.What is the sum of the first 11 odd numbers (1 + 3 + 5 + …)? (a) 132 (b) 21 (c) 121 (d) 66
  28. 28.What is the sum of the first 9 terms of the AP 7, 12, 17, …? (a) 47 (b) 243 (c) 248 (d) 486
  29. 29.What is the sum of the first 20 odd numbers (1 + 3 + 5 + …)? (a) 210 (b) 39 (c) 420 (d) 400
  30. 30.What is the sum of the first 27 odd numbers (1 + 3 + 5 + …)? (a) 756 (b) 53 (c) 729 (d) 378
  31. 31.What is the 34th term of the AP 7, 11, 15, 19, …? (a) 143 (b) 139 (c) 132 (d) 136
  32. 32.What is the sum of the first 5 terms of the AP 2, 4, 6, …? (a) 35 (b) 10 (c) 60 (d) 30
  33. 33.What is the sum of the first 11 terms of the AP 1, 2, 3, …? (a) 66 (b) 67 (c) 11 (d) 132
  34. 34.Which term of the AP 5, 9, 13, 17, … is 133? (a) 34th (b) 32nd (c) 35th (d) 33rd
  35. 35.What is the 29th term of the AP 2, 6, 10, 14, …? (a) 112 (b) 118 (c) 116 (d) 114
  36. 36.What is the 20th term of the AP 1, 7, 13, 19, …? (a) 120 (b) 114 (c) 115 (d) 121
  37. 37.What is the sum of the first 7 terms of the AP 3, 9, 15, …? (a) 294 (b) 39 (c) 168 (d) 147
  38. 38.What is the sum of the first 6 terms of the AP 9, 12, 15, …? (a) 24 (b) 108 (c) 198 (d) 99
  39. 39.Which term of the AP 4, 6, 8, 10, … is 22? (a) 10th (b) 11th (c) 12th (d) 9th
  40. 40.What is the sum of the first 6 terms of the AP 7, 9, 11, …? (a) 144 (b) 78 (c) 72 (d) 17

Answer key

  1. 96
  2. 73
  3. 189
  4. 126
  5. 140
  6. 216
  7. 31st
  8. 128
  9. 72
  10. 625
  11. 24th
  12. 19
  13. 60
  14. 16
  15. 3160
  16. 900
  17. 68
  18. 90
  19. 25
  20. 55
  21. 1830
  22. 125
  23. 2145
  24. 65
  25. 30
  26. 3655
  27. 121
  28. 243
  29. 400
  30. 729
  31. 139
  32. 30
  33. 66
  34. 33rd
  35. 114
  36. 115
  37. 147
  38. 99
  39. 10th
  40. 72

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